Application to geophysics: Challenges and some solutions Andrew Binley Email: a.binley@lancaster.ac.uk

Hydrogeophysics – the drivers Characterising groundwater systems is challenging because of the (physical and chemical) complexity of the shallow subsurface and the difficulty in observing the structure of the system … Hartman et al. (2007) … and the complex response due to external loading. Robin Nimmer, Moscow, Idaho

Hydrogeophysics – the drivers Geophysics has been widely used to support groundwater investigations for many years. However, many of the earlier approaches concentrated on using geophysics to define lithological boundaries and other subsurface structures. Resistivity profile and hydrogeological section, Penitencia, CA (after Zohdy, 1964).

Hydrogeophysics – the drivers During the 1990s there was a rapid growth in the use of geophysics to provide quantitative information about hydrological properties and processes. Much of this was driven by: - the recognition of the importance of heterogeneity of subsurface properties that influence mass transport in groundwater systems. - the need to gain information of direct value to hydrological models, particularly given the developments of ‘data hungry’ stochastic hydrology tools. Tiedeman & Hsieh (2004)

Hydrogeophysical approach Static imaging Dynamic imaging Rock physics model(s) Rock physics model(s) structure (e.g. permeability maps) process (e.g. transport of solute) Kemna (2003) Kowalsky et al. (2006) Improved hydrogeological model

Hydrogeophysical approach Resolution Airborne Surface imaging Cross-borehole imaging Well logs Core imaging Micro- structure Survey scale

Commonly used approach – static imaging Boise, Idaho , USA 14m log10 (resistivity, in Wm) 2.3 3.2 Keery, Binley, Slater, Barrash and Cardiff (in prep)

Commonly used approach – dynamic imaging Hatfield, UK Monitoring changes in resistivity due to tracer injection. Ultimately to understand pathways of solutes from ground surface to the aquifer. 15-Mar-03 Depth (m) Distance (m) 16-Mar-03 Depth (m) Distance (m) 21-Mar-03 Depth (m) Distance (m) Depth (m) Distance (m) 24-Mar-03 Depth (m) Distance (m) 27-Mar-03 Depth (m) Distance (m) 02-Apr-03 H - E4 E2 R2 I2 R1 E1 - Tracer injected at H-I2 - - - - H H H H H H - E3 Winship, Binley and Gomez (2006)

Challenge 1: Larger scale application But many of the hydrological challenges are at a larger scale

Larger scale example Objective: determine potential connectivity between land surface and regional sandstone aquifer Elevation (m above sea level)

Larger scale example Electromagnetic (EM) conductivity surveys reveal variation over top 6m

Larger scale example Electrical resistivity tomography (ERT) provides an assessment of vertical structure C+ C- P+ P- C+ C- P+ P- C+ C- P+ P- C+ C- P+ P- C+ C- P+ P- C+ C- P+ P- C+ C- P+ P- C+ C- P+ P- Current is injected between C+ and C- The voltage difference between P+ and P- is measured The voltage difference is a function of the current injected and the resistivity beneath the electrode array

Larger scale example Window in the clay? Clayey drift Sandstone stream Conductivity (mS/m) log10 (resistivity, in Wm)

Challenge 2: Data fusion Resistivity & Induced Polarisation GPR Borehole logs Ground Conductivity Local sampling and geology How do we bring all these data together to form one consistent, improved model of the system?

Challenge 2: Data fusion Can we use other information to help constrain the inversion of geophysical data? For example, we may be able to estimate spatial covariance structure based on well log data? Linde, Binley, Tryggvason, Pedersen and Revil (2006)

Challenge 2: Data fusion We could jointly invert the two (or more) data using a structural similarity, e.g. by minimising the cross-gradients operator In areas where the gradients are in the same or opposite direction (or where one of the gradients is zero) t will be zero (and the pixels structurally similar) Gallardo (2006)

Challenge 2: Data fusion We cannot use geophysical imaging alone – we need to use geophysics to support other data (not replace it) Static imaging Measurements of hydrological states Rock physics model(s) Well log data structure (e.g. permeability maps)

Challenge 3: Assessing information content At times there is a need to assess information content in data (this has been significantly overlooked to date) Understanding the value of different information will permit appropriate resource allocation to the project and help with survey design. This is becoming more and more relevant as large hydrological projects invest in hydrogeophysical surveys. £X drilling £X geophysics

Data fusion Geophysical method Inversion (McMC) Output ERT   EM Parameter resolution Quantified information Mapping Spatial resolution GPR Other methods Prior information Uncertainties

Data fusion Site represented as series of 1D models Permits practical application of Markov chain Monte Carlo (McMC) Bayes’ theorem Joint likelihood function Misfit Likelihood MH sampling (accept/reject) Prior Posterior

Data fusion Increase in information as uncertainty in property reduces (e.g., Maurer et al., 2010) Shannon’s Entropy (Shannon, 1948) Increase in information as uncertainty in property reduces (Shannon’s Entropy) Information

(Lagrange multipliers method) Data fusion Bayesian Maximum Entropy (BME) Serre & Christakos (1999) BMELIB (http://www.unc.edu/depts/case/BMELIB/) Expected knowledge Maximization (Lagrange multipliers method)   Prediction Hard data (Information >2) Soft data (Information <2) G: general knowledge S: site-specific knowledge K: total knowledge Christakos (2000) Predicted pdf

Data fusion 1D synthetic example showing how different data provides constraint to resistivity structure JafarGandomi & Binley (in review)

Data fusion Example data fusion on quasi 2D profile from Trecate, Italy Distance (m)

e.g. permeability structure Coupled hydrogeophysical inversion Surely we know something about the hydrology? And, if so, then we should use this in our inversion Hydrological model ? Geophysical surveys (assumed known) Rock physics model(s) Hydrological model, e.g. permeability structure Inversion

Coupled hydrogeophysical inversion Do we need to invert geophysical data? We have been exploring the potential of using geophysical data (not images) as a means of constraining hydrological models in an McMC framework. Scholer, Irving, Binley and Holliger (2011)

Coupled hydrogeophysical inversion Prior distribution for the 4 hydrological model parameters Posterior distribution for the 4 hydrological model parameters for each of the 4 layers Scholer, Irving, Binley and Holliger (2011)

Summary Deterministic inversion of 3D geophysical data is now relatively common, although the assessment of uncertainty is lacking. Attempts have been made to jointly invert geophysical data, although most of these have been done in 2D. We need to develop ways of combining multiple data (multiple scales). These fusion approaches must allow some assessment of information value, particularly as we look at new survey designs (for future data). Attempts have been made to use geophysical data within a hydrological model inversion. So far these have been limited to relatively low dimensional models.